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The Convective instability of non-Newtonian of boundary-layer flow over rough rotating-disk

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thesis
posted on 17.06.2022, 13:30 authored by Aishah Alqarni

This thesis considers the local linear convective stability behaviour of non- Newtonian boundary-layer flows over rotating disks and the effects of surface roughness. A non-Newtonian fluid is modelled via the Carreau model, which represents a type of generalised Newtonian fluid. Using the Carreau model for a range of shear-thinning and shear-thickening fluids, we determine, for the first time, steady-flow profiles under the partial-slip model for surface roughness.The partial-slip approach of Miklavčič & Wang [1] is modified in such a way that the viscosity is no longer constant and depends on the shear rate. The non-linear ordinary differential equations are reduced via the introduction of a suitable similarity solution. The stability equations are solved to obtain the disturbance eigenfunctions and to plot curves showing neutral stability using the Chebyshev collocation method. The stability of a non-Newtonian boundary-layer flows is investigated with different boundary conditions: the no-slip boundary conditions and the partial-slip. Thereby the neutral curves for the convective instabilities associated with the boundary-layer flow due to a rotating disk can be determined over a broad range of parameter values. The subsequent linear stability analyses of these flows indicate that isotropic and azimuthally anisotropic surface roughness leads to the stabilisation of both shear-thinning and -thickening fluids. This is evident in the behaviour of the critical Reynolds number and growth rates of both Type I (inviscid cross flow) and Type II (viscous streamline curvature) modes of instability. The underlying physical mechanisms are clarified using an integral energy equation.

History

Supervisor(s)

Stephen Garrett

Date of award

03/05/2022

Author affiliation

Department of Engineering

Awarding institution

University of Leicester

Qualification level

Doctoral

Qualification name

PhD

Language

en